Exactly solvable phase oscillator models with synchronization dynamics

Details Exactly solvable phase oscillator models with synchronization dynamics Exactly solvable phase oscillator models with synchronization dynamics

1998-03-04

arxiv.org/abs/cond-mat/9803055v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures, Revtex file

Scientific paper

10.1103/PhysRevLett.81.3643

Populations of phase oscillators interacting globally through a general coupling function $f(x)$ have been considered. In the absence of precessing frequencies and for odd-coupling functions there exists a Lyapunov functional and the probability density evolves toward stable stationary states described by an equilibrium measure. We have then proposed a family of exactly solvable models with singular couplings which synchronize more easily as the coupling becomes less singular. The stationary solutions of the least singular coupling considered, $f(x)=$ sign$(x)$, have been found analytically in terms of elliptic functions. This last case is one of the few non trivial models for synchronization dynamics which can be analytically solved.

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